As was argued in [1]}, for one of the two string realizations of the 9-dimensional neutral domain wall that we are aware of, namely the type I non-BPS D8-brane, the breaking is not expected.
In this case, the symmetry has to be gauged.
Indeed, it is known that type I (non-BPS) Dp-branes are classified by KO-theory [2]}, [3]}.
In particular, a non-BPS D8 brane is associated to KO\(^{-1}\) (pt)\(\,=\!\mathbb {Z}_2\) .
Via the Atiyah-Bott-Shapiro orientation, this group is indeed isomorphic to \(\Omega _1^{\rm Spin}\) .
However, as proposed in [1]}, in this peculiar case the cobordism invariant contribution to the \(\mathbb {Z}_2\) -valued tadpole cancellation condition vanish (mod 2).
Thus, gauging the global \(\mathbb {Z}_2\)  symmetry we started with requires an even number of non-BPS D8 brane charges to cancel the tadpole on the KO-theory side.
